Patricio Felmer dicta charla magistral en la UC sobre resolución de problemas matemáticos

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Invitado por el Equipo de Didáctica de la Matemática de la Facultad de Educación UC, el Premio Nacional de Ciencias Exactas chileno postuló que la resolución de problemas debe estar en el corazón de las clases de la asignatura, describió las múltiples competencias y habilidades que desarrolla y reivindicó el valor del error, frente a un auditorio repleto de profesores en ejercicio de la disciplina.

El reconocido matemático fue invitado a la Facultad de Educación de la UC para dictar la clase “La Resolución de Problemas: el corazón de la Matemática”, organizada por el equipo de Didáctica de esta disciplina compuesto por los profesores Horacio Solar y el sub director de Docencia, Francisco Rojas, y quienes desde el 2015 desarrollan un ciclo de conversaciones sobre este campo.

En su charla, que tuvo lugar en el Campus San Joaquín el pasado 19 de julio, Felmer afirmó que en las clases de matemática de nuestro país no existe ni se ejercita la resolución de problemas. “¿Y en qué se sustenta esta afirmación? En algunos artículos de investigación (pocos), en mi experiencia personal y en la experiencia de personas que conozco, incluyendo todas las salas de clase que he visto”, declaró.

-En las clases de matemática de nuestro país, los niños y niñas no resuelven problemas. ¿Y qué nos pasa hoy? Los estudiantes no se motivan, o se preguntan para qué sirve. Se acepta que un grupo grande no participe del aprendizaje de la matemática, e incluso se acepta socialmente que alguien nunca fue bueno para la matemática –caracterizó. Es un panorama desalentador, agregó.

Felmer recordó que en clases de Música, Artes o Actividad Física, es natural que los niños intenten hacer por sí mismos lo que hacen los expertos de cada disciplina: en la clase de música, hay que saber tocar instrumentos, y en las clases de gimnasia jugar básquetbol o fútbol lo mejor que uno pueda hacerlo. “Entonces, por qué no dedicar la clase de matemática a resolver problemas? ¡Eso es lo interesante!” subrayó.

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Felmer preguntó al auditorio repleto de profesores en ejercicio qué es lo interesante para los matemáticos, qué los emociona, qué los frustra y qué los pone contentos.

-Nuestra hipótesis es que a los matemáticos les produce emoción resolver problemas. Resuelven los problemas que les interesan. Les gustan los desafíos, pero no los imposibles, sino los que se pueden abordar. Jamás se entretienen con un problema que ya está resuelto o que es parecido a uno resuelto. Los matemáticos planteamos y resolvemos problemas – definió.

Ganancias

En el ejercicio de resolver problemas, un estudiante puede adquirir distintas habilidades y competencias, afirmó el Premio Nacional de Ciencias Exactas.

-Por ejemplo, la "inducción". Es decir, estudiar ejemplos, tantos como sea necesario, y entonces adivinar un patrón, una generalización. Esto se logra mediante un ejercicio permanente de adivinar y demostrar, de conjeturar y probar. También está la analogía, y está hacer diagramas, gráficos y todo tipo de ilustraciones que permitan razonar o comprender situaciones más complejas o abstractas, caracterizó.

Más adelante, Felmer caracterizó el problema ideal. “Los problemas interesantes son aquellos que desafían, que no se sabe cómo resolverlos, que no hay un método para hacerlo… Un problema es una actividad matemática para la cual la persona que la enfrenta no conoce un procedimiento que le conduzca a la solución. Si un profesor plantea un problema a la clase y la alumna o alumno más aventajado del grupo lo logra resolver por sí mismo, es que no estamos desafiando suficientemente a la clase” argumentó.

Felmer también sostuvo que nuestro país está muy empeñado en evitar las equivocaciones dentro del aula, pero que estas forman parte integral de todo proceso de aprendizaje.

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“Los errores son una parte normal del aprendizaje. Los errores son también una buena forma de ver dónde están las dificultades, te muestran que no estás trabajando en un problema que es muy fácil, para saber que no estás perdiendo el tiempo. Si no cometes errores, entonces, no estás trabajando en el problema correcto”, aseveró.

Patricio Felmer también indicó que los humanos siempre hemos planteado y resuelto problemas, que forma parte de nuestra esencia y que estamos hechos para ello.“Es nuestra estrategia de sobrevivencia, nuestra herramienta de desarrollo”, decretó.

-La Resolución de Problemas debe estar siempre en las clases de matemática de nuestras escuelas. Posibilita la autonomía en el conocimiento, la creatividad frente a situaciones nuevas y el uso flexible de los contenidos matemáticos. También favorece la comunicación de ideas matemáticas, el razonamiento, el trabajo en colaboración con pares y la perseverancia frente a las dificultades”, concluyó.

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Patricio Felmer, destacado experto del Centro de Investigación Avanzada en Educación de la Universidad de Chile (CIAE), lidera la iniciativa ARPA (“Activando la Resolución de Problemas en las Aulas”), cuyo sitio web es www.arpamat.cl

Texto: Francisco Zabaleta, Facultad de Educación UC

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1 × SELECT `path` FROM educacion_rsfirewall_ignored
1 × SELECT id, rules FROM `educacion_viewlevels
1 × SELECT b.id FROM educacion_usergroups AS a LEFT JOIN educacion_usergroups AS b ON b.lft <= a.lft AND b.rgt >= a.rgt
1 × SELECT `session_id` FROM `educacion_session`
1 × SELECT `file` FROM educacion_rsfirewall_hashes
1 × SELECT * FROM educacion_rsfirewall_configuratio
1 × SELECT alias, catid FROM educacion_content
1 × SELECT `params` FROM educacion_extensions
1 × SELECT m.id, m.menutype, m.title, m.alias, m.note, m.path AS route, m.link, m.type, m.level, m.language,m.browserNav, m.access, m.params, m.home, m.img, m.template_style_id, m.component_id, m.parent_id,e.element as component FROM educacion_menu AS m LEFT JOIN educacion_extensions AS e ON m.component_id = e.extension_id
1 × SELECT * FROM educacion_languages
1 × SELECT `data` FROM `educacion_session`

OTRAS Tablas:

1 × UPDATE `educacion_session` SET `data` = '__default|a:8:{s:15:\"session.counter\";i:1;s:19:\"session.timer.start\";i:1743814893;s:18:\"session.timer.last\";i:1743814893;s:17:\"session.timer.now\";i:1743814893;s:24:\"session.client.forwarded\";s:13:\"13.58.149.106\";s:8:\"registry\";O:9:\"JRegistry\":1:{s:7:\"\0*\0data\";O:8:\"stdClass\":0:{}}s:4:\"user\";O:5:\"JUser\":25:{s:9:\"\0*\0isRoot\";b:0;s:2:\"id\";i:0;s:4:\"name\";N;s:8:\"username\";N;s:5:\"email\";N;s:8:\"password\";N;s:14:\"password_clear\";s:0:\"\";s:8:\"usertype\";N;s:5:\"block\";N;s:9:\"sendEmail\";i:0;s:12:\"registerDate\";N;s:13:\"lastvisitDate\";N;s:10:\"activation\";N;s:6:\"params\";N;s:6:\"groups\";a:0:{}s:5:\"guest\";i:1;s:13:\"lastResetTime\";N;s:10:\"resetCount\";N;s:10:\"\0*\0_params\";O:9:\"JRegistry\":1:{s:7:\"\0*\0data\";O:8:\"stdClass\":0:{}}s:14:\"\0*\0_authGroups\";a:1:{i:0;i:1;}s:14:\"\0*\0_authLevels\";a:2:{i:0;i:1;i:1;i:1;}s:15:\"\0*\0_authActions\";N;s:12:\"\0*\0_errorMsg\";N;s:10:\"\0*\0_errors\";a:0:{}s:3:\"aid\";i:0;}s:20:\"com_rsfirewall.geoip\";s:2:\"US\";}' , `time` = '1743814895'
1 × UPDATE educacion_content SET hits = hits + 1
1 × SHOW FULL COLUMNS FROM `educacion_rsfirewall_logs
1 × INSERT INTO `educacion_session` (`session_id`, `client_id`, `time`) VALUES ('985760cd6731280af74c5173eaf181fd', 0, '1743814893'
1 × DELETE FROM `educacion_session`

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Registro Database

45 Registro Consultas

35 Tipos de consultas del registro, Ordenado por acontecimientos.

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